To be honest, even transiting in a one-stop situation in Saudi Arabia can get screwed up. Really, I would rather fly EK to DXB or QR to DOH, backtrack to JED for Umra, then travel onwards to KHI via EK or QR than deal with the unpredictability of Saudia.

So, Saudia or a travel agent sold you the current ticket and that entity is the one that needs to make the change free of charge. If this tack fails (and it shouldn't), just pester the Saudia office in MED or KHI to make the necessary changes. If they don't, just buy a cheap one way KHI-IAD on your return.

Another option might be to apply for an Umra visa when you arrive in KHI, so that you can do the international to domestic transfer in DMM, but they might want to see a ticket and they might have a 3-5 day turnaround time. Like all things to do with Saudi Arabia, what happens to you really is up to the person you are dealing with at the time. Good luck, and lesson learned, right?